Will these bulbs work?

Electrically they should be fine. It would be good to know what a BA9S socket is to make sure they will fit physically.

They might be too big, since they say they are for the side marker lights on a car.

From Wikipedia

Bob, I don't know about your 022 switches, but some in my stockpile are bayonet base and some screw base.  I just pulled out 9 of the switches to construct a layout for my grandson, and bought red, green, & white LEDs to eliminate the heat and cut needed transformer size.  I paid $2/bulb at York from Town & Country, avoiding their $9 or $10 shipping charge.  One problem I have encountered, which I was also encountering with some incandescent white bulbs I had, is that I can't push them in far enough to get the bayonet studs to twist & engage.

ARe you certain these bulbs are replacements for 1445 & 1447?

You don't have to go to LED's. If you use 2445 bulbs (24-volt) in your switches you can run them at a sufficiently high voltage so they snap over smartly but the bulbs won't burn so hot that they melt the lanterns. 2447 is the screw-base version if you have some of the older 022's. 

Another reason for LED's is the current consumption.  Even running higher voltage bulbs, they will consume multiple times what an LED bulb will consume.  If you have enough switches, that ends up being real power.

Thanks guys. They actually list the measurements of the bulb on the website and it appears to be an exact fit. I did look at Town and Country and as was mentioned the shipping is $10 flat rate, so for just a couple of bulbs it really raises the price. Based on what everyone has said I think I'll order some of these and then report back once I get them to let you know how I made out. I have to search for a couple of the screw type too. Thanks everyone.

Some preliminary research suggests that BA9S is the correct size base.

Try this link:

http://www.mts.net/~william5/library/minilamp.htm

If you like the hand-made look.  eBay # 171870074870

Engineer Bob how are you handling the fact that the bulbs are DC and not AC which is what Lionel transformers put out ??

I've been told that AC vs. DC is not a problem at this low voltage. Update: The slow boat from China wasn't so slow after all. I got the bulbs in less than 2 weeks. They work just fine. They are a cool white rather than a warm white so they are just a touch dimmer than what I had before but not by much at all. I'm very pleased with the result and you can't beat the price.